The evolution of x-ray computed tomography (CT) has produced scanners with decreasing data acquisition and image reconstruction times and increasing density and spatial resolutions. The improvements have been achieved primarily by the use of more sophisticated data acquisition systems and faster image reconstruction hardware. A second means for improving the image quality has been to reevaluate assumptions made in order to build the early generations of CT scanners and to incorporate corrections within the image reconstruction algorithm. These assumptions were made in order for the data collected by an actual scanner to be compatible with theoreitcal reconstruction algorithms.
An example of these engineering assumptions has to do with the spectrum of the x-ray source and the energy dependence of the attenuation coefficients of different elements of the object under examination. An important assumption used in the past to produce images is that the source is monochromatic or that the energy dependence of the attenuation coefficients is identical for all elements. It is well known that neither of these two conditions is satisfied and hence what is known as polychromatic artifacts are produced in resulting images. The artifacts can be identified as cupping and as negative streaks between sharp objects that have high attenuation coefficients.
The prior art, see for example U.S. Pat. No. 4,217,641, uses an iterative post-reconstruction method to reduce the level of polychromatic artifacts. Among other known prior art describing polychromatic artifact correction techniques are: U.S. Pat. Nos. 4,222,104 and 4,223,384 as well as an article entitled "A Framework for Spectral Artifact Corrections in X-ray Computed Tomography," by J. Peter Stonestrom, et. al., in the IEEE Transactions on Biomedical Engineering, Vol. BME-28, No. 2, February 1981.
The basis of these prior art post-reconstruction correction methods is that objects are made up of two approximately homogeneous components with respect to the energy dependence of their attenuation coefficients. In biological applications the two components are bone and soft tissue. An initial image is reconstructed incorporating first-order polychromatic corrections for the majority element, usually soft tissue. The initial image is then segmented on a pixel-by-pixel basis in order to generate approximate images of the two components. The path lengths are then calculated through the two images using reprojection techniques. Error projections are then formed from the reprojections and added to the projection data that was used to form the initial image. A second-order image is then reconstructed from the new projection data. If the level of polychromatic correction is sufficient, then the algorithm is complete. If not, the above procedure is repeated.
The use of reprojection is not limited to polychromatic correction algorithms. The paper "An Algorithm for the Reduction of Metal Clip Artifacts in CT Reconstructions," by G. H. Glover and N. J. Pelc, in Medical Physics, Vol. 8, No. 6, November 1981, presents a method to remove the artifacts caused by metal clips using reprojejction as part of their algorithm. The paper "A Simple Computational Method for Reducing Streak Artifacts in CT Images," by G. Henrich, in Computed Tomography, Vol. 4, 1981, describes an algorithm that can be used to remove streaks such as those caused by partial volume artifacts.
The polychromtic-, metal clip-, and streak-artifact correction algorithms described in the prior art have not been implemented commercially because the reprojection step has been extremely time-consuming. The prior art reprojection methods have been too slow because they have relied upon the inherent reprojection step incorporated in the reconstruction algorithms based on algebraic techniques. The slowness of the prior art reprojection systems and an attempted solution are highlighted in a paper "Algorithms for Fast Back- and Re-projection in Computed Tomography," by T. M. Peters, in IEEE Transactions on Nuclear Science, Vol. NS-28, No. 4, August 1981. The paper presents a method that uses a modified backprojector to obtain reprojections. The problem with this system is that the modifications radically change the hardware of a backprojector and thus the system is not readily applicable to commercially installed CT units. The system requires means to reverse the normal data flow through the backprojector, resulting in reprojections at the normal input of the unit. In addition to the need for changed hardware, the resulting reprojections are of poor quality and require complex corrections in order to use them with an artifact correction algorithm.
Accordingly there is a long-standing need for fast reprojection techniques and equipment.